The crisis which struck the global financial markets between 2007 and 2012 and that is still showing its impact, has revealed the need for new advanced studies concerning Systemic Risk and Dependency Structures in the financial market. One of the key concept for these studies is "interconnectedness" and, more in the specific, the understanding of the relation of dependence between the different institutions in the considered system. One way that statistics has to meet this need are the so called "Copula models". Because of their flexibility and their relatively accessible implementation, some simple versions of these models, like the Gaussian ones, became the reference methods for systemic risk valuations. The inappropriate employment of these models to model the dependence structures, is considered as one of the concauses of the underestimation of the growing danger in the months prior the beginning of the crisis. The need to improve, brought to a significant increase in the level of interest from the research community in the refinement and the enrichment of these methodologies. Numerous studies showed evidences about a time evolution in the correlation structure between equity returns, leading to the development of a research stream aiming to involve conditioning variables in copula models. In this way the description of the dependence structure can be adapted to the different market conditions which are going to have a direct impact on the intra-firms performances influence. A key point in the concept of systemic risk is the fact that it refers to a composite entity: from the perspective of modelling, this means that we need to operate with a large number of variables at the same time. To do so, the use of factor models came as one of the most immediate solutions also in the copula modelling framework. In view of the above, we will provide a theoretical introduction about copula models, their basics properties and applications. We will then have a deeper insight concerning the time dependent models and the ones based on an underlying factor structure. Joining these specifications with the one of the GAS model, employed for the dynamic evolution, we get a dynamic factor copula in line with the one introduced by Oh and Patton (2016). With the support of this model, we are going to present a case study focused on systemic risk in the banking system. Our data set is composed of 5 years CDS spreads, employed to describe the health state of the banks institutions to which they are referred. We will give an exhaustive statistical description of the data set to then exploit the previously defined models to produce specific systemic-risk measures estimations, obtaining a description of the systemic risk evolution over the considered time period. «

The crisis which struck the global financial markets between 2007 and 2012 and that is still showing its impact, has revealed the need for new advanced studies concerning Systemic Risk and Dependency Structures in the financial market. One of the key concept for these studies is "interconnectedness" and, more in the specific, the understanding of the relation of dependence between the different institutions in the considered system. One way that statistics has to meet this need are the so called... »